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The Maxima on-line user's manual

Algebra Calculator

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Trigexpand Calculator

Trigexpand

Function: trigexpand (<expr>) Expands trigonometric and hyperbolic functions of sums of angles and of multiple angles occurring in <expr>. For best results, <expr> should be expanded. To enhance user control of simplification, this function expands only one level at a time, expanding sums of angles or multiple angles. To obtain full expansion into sines and cosines immediately, set the switch trigexpand: true.

f:tan(2*u-v);
f:trigexpand(f);

trigexpand is governed by the following global flags:

trigexpand If true causes expansion of all expressions containing sins and coss occurring subsequently.

halfangles If true causes half-angles to be simplified away.

trigexpandplus Controls the "sum" rule for trigexpand, expansion of sums (e.g. sin(x + y)) will take place only if trigexpandplus is true.

trigexpandtimes Controls the "product" rule for trigexpand, expansion of products (e.g. sin(2 x)) will take place only if trigexpandtimes is true.

Examples:

          (%i1) x+sin(3*x)/sin(x),trigexpand=true,expand;
                                   2           2
          (%o1)               - sin (x) + 3 cos (x) + x
          (%i2) trigexpand(sin(10*x+y));
          (%o2)          cos(10 x) sin(y) + sin(10 x) cos(y)

There are also some inexact matches for trigexpand. Try ?? trigexpand to see them.

(%o1)                                true
(%i2) 

Trigexpand Example

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